What is the influence of long excitation pulses on the relationship between luminescence intensity and the excitation intensity (Bimolecular process)?

In the luminescence processes (Bimolecular process), if long excitation pulses were used, and after a transient initial increase in luminescence intensity, i(t), the steady-state value of intensity is still looks like $$i(0)=\left(\frac{\beta_{\text{r}}}{\beta_{\text{r}}+\beta_{\text{nr}}}\right)G = \left(\frac{\beta_{\text{r}}}{\beta_{\text{r}}+\beta_{\text{nr}}}\right)\alpha I_{\text{ex}}$$

(same like the short excitation pulses). Why?